University of Alberta Local Oscillator and Focal Distance Measurement System for the Square Kilometre Array Leonid Belostotski O A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science Department of Electrical and Cornputer Engineering Edmonton, Alberta Spnng 2000 National tibraiy Bibliothéque nationale du Canada Acquisitions and Acquisitions et Bibliographie Services seMces bibliographiques The author has granted a non- L'auteur a accordé une licence non exclusive licence allowing the exclusive permettant a la National Library of Canada to Biblioth6que nationale du Canada de reproduce, loan, distri'bute or seil reproduire, prêter, distri'buer ou copies of this thesis in microfom, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/nlm, de reproduction sur papier ou sur format électronique. The author retains ownefihip of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protége cette thèse. thesis nor substantial exûacts fiorn it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permi:ssion. autorisation. ABSTRACT A systern which sirnultaneously provides coherent local oscillator signal and mea- sures focal length for the Large Adaptive Reflector is discussed. The Local Oscillator subsystem provides a phasestable signal to an airborne platform over a radio Iink. A phase stability of 5"ms at 22 GHz is the goal for the system. Feedback is em- ployed to readjust the phase of the delivered signal, to compensate for changes in the transmission medium. The dynsmic properties of the Local Oscillator system are controlled primarily by a phase-locked Ioop. A Focal Length Measurement subsys- tem employing the Chinese remainder theorem for ambiguity resolution is proposed. The subsystem will measure the focal distance of 500 m with an accuracy of 70 Pm. Both systems are based on interferometric techniques and are combined into one. A prototype of the Local Oscillator subsystem has been built and tested to demonstrate feasibility of the concept. I would like to thank al1 people who helped me with this thesis in any way. 1 thank the staff of the Dominion Radio Astrophysicd Observatory for being very helpful and friendly. 1 would like to thank my supervison Dr. Tom Landecker, Dr. Dave Routledge, and Dr. Fked Vaneldik for helping me through digerent stumbling blocks I ran into while working on the thesis. 1 would like to thank Dr. Peter Dewdney and Dr. Bruce Veidt for lots of advice and for making the work on the Square Kilometre Array and the Large Adaptive Reflector continue. 1 thank Rod Stuart, Ron Casono, Jean Bastien, and Ron McDougall for helping me build my systern. 1 thank Brian Force for mentioning the "Chinese numbers" which eventually led to employment of the Chinese remainder theorem in my system. 1 would like to thank Anne Guerra for helping with editing the thesis and with different problems encountered along the way. 1would like to thank programmers who created LyX the document processor that made writing this thesis easier. Contents Abstract Acknowledgment List of Figures List of Tables Glossary able of Symbols 1 Background 1.1 Introduction . 1 1.2 The Square Kilometre Array . 2 1.3 The Large Adaptive Reflector telescope . 4 1.3.1 A Local Oscillator system and a Focal Length measurement system . 6 1.3.2 Location of the FLLOSS witbin the LAR telescope . 7 1.4 FLLOSS specifications . 7 1.5 Thesis layout . 8 2 Distance measurement systems 9 2.1 Introduction . 9 2.2 Background ................................ 9 2.2.1 Distance measurement ...................... 9 2.2.2 Pseudo-random noise ...................... 10 2.2.2.1 PRN selection ...................... 10 2.2.2.2 PRN generation .................... 11 2.2.2.3 Delay measurement using PRN ............ 12 2.2.3 Atmosphenc effects ........................ 13 2.2.4 Cycle slips, Multipath and Doppler shiR ............ 14 2.2.5 System noise ........................... 15 2.2.6 Linear combination of signal phases ............... 15 2.3 Summary of digerent ranging systems .................. 15 2.3.1 Laser-based rangingsystems ................... 15 2.3.2 RF pulse technique ........................ 16 2.3.3 Correlator techniques ....................... 16 2.3.3.1 Wideband noise modulation ............. 16 2.3.3.2 Sinusoidal sweep frequency modulation ........ 18 2.3.3.3 Bandwidth synthesis .................. 18 2.3.4 Tellurometer distance measurernent scheme ........... 19 2.3.4.1 System structure .................... 19 2.3.4.2 System operation .................... 19 2.3.5 Global Positioning System .................... 22 2.3.5.1 GPS signal structure .................. 22 2.3.5.2 Code Pseudorange ................... 23 2.3.5.3 Phase Pseudorange ................... 23 2.3.5.4 Distance Measurement ................. 24 2.4 Measurement accuracy .......................... 26 2.4.1 Laser-based devices ........................ 26 2.4.2 Wideband noise modulation ................... 27 2.4.3 Sinusoidal sweep frequency modulation ............. 27 2.4.4 Bandwidth synthesis ....................... 27 2.4.5 Tellurorneter ............................ 28 2.5 Sensitivity to errors ............................ 28 2.5.1 Laser-based systems ....................... 28 2.5.2 Correlat or-based systems ..................... 28 2.5.3 Phase measuring systems ..................... 28 2.6 Conclusion ................................. 29 3 Local OsciIlator System 31 3.1 Introduction ................................ 31 3.2 Background: Control systems ...................... 31 3.2.1 Control system theory ...................... 32 3.2.1.1 S-plane domain ..................... 33 3.2.1.2 Fkequency response domain .............. 34 3.2.1.3 Sime domain specincations .............. 37 3.2.1.4 Phase Locked Loop ................... 37 3.3 Summary of existing LO systems .................... 38 3.3.1 Swarup and Yang LO system .................. 38 3.3.2 Cascaded PLL system ...................... 38 3.3.3 Automatically Correcting system ................ 39 3.3.4 Spatially Distributed PLL system ................ 40 3.3.5 Discussion ............................. 41 3.4 Cornparison of the Cascaded PLL and Spatially Distributed systems . 41 3.4.1 Cornparison of steady-state errors due to distance changes . 41 3.4.1.1 Spatidly Distributed PLL system ........... 41 3.4.1.2 Cascaded PLL system ................. 44 3.4.2 Stability in the presence of time delay .............. 47 3.4.3 Distance Measurernent ...................... 48 3.5 Conclusions ................................ 48 4 The Focal Length/LO system 50 4.1 Introduction ................................ 50 4.2 Background: Chinese rernainder theorem ................ 50 4.3 Combining the LO and FLM systems .................. 51 4.4 Selection of the frequencies of operation ................. 60 4.5 Procedure for distance measurement .................. 62 4.6 Other design issues ............................ 65 4.6.1 Calibration ............................ 65 4.6 -2 Fkequency of distance measurements .............. 66 4.6.3 Phase measurement accuracy .................. 66 4.6.4 Minimum signal to noise ratio .................. 67 4.6.5 Antennas ............................. 69 4.7 Conclusion ................................. 70 5 LO system prototype design 71 5.1 Introduction ................................ 71 5.2 Background ................................ 71 5.2.1 Link budget and signal to noise ratio .............. 71 5.2.2 Effect of impedance mismatches on signal phases ....... 72 5.3 LO prototype design ........................... 73 5.3.1 Selection of frequencies for use in LO prototype ........ 73 5.3.2 Preliminary prototype configuration discussion ......... 74 5.3.3 Noise Considerations for the LO system ............ 75 5.3.3.1 Noise introduced in phase-halving PLL ........ 75 5.3.3.2 Noise acquired in the uplink .............. 76 5.3.3.3 Noise acquired in the downlink ............ 77 5.3.3.4 Noise due to the motion of airborne platform .... 78 5.3.4 LO prototype simulations .................... 79 5.3.5 Phase-halving PLL design .................... 85 5.3.5.1 Component selection .................. 85 5.3.5.2 PLL loop filter design ................. 87 5.4 Lu prototype impiementation ...................... 87 5.4.1 PLL implementation ....................... 87 5.4.1.1 Phasehalving PLL phase stability meanirement ... 87 5.4.2 Antenna design and implernentation ............... 88 5.4.2.1 Feed design ....................... 88 5.4.2.2 Paraboloidal antenna performance measurement ... 95 5.4.3 LO prototype testing ....................... 99 5.4.3.1 Link budget for 800 metre test ............ 101 5.4.3.2 Link budget for 350 metre test ............ 106 5.5 LO system performance ......................... 110 5.5.1 LO prototype test without time delay ..............110 5.5.1.1 Improvement of the LO performance .........111 5.5.2 100 metre test ...........................112 5.5.3 350 metre test ........................... 117 5.5.4 800 metre test ........................... 121 5.6 Discussion ................................. 125 6 Conclusion 127 Bibliography 129 A Remote unit and ground unit circuit diagrams 134 B Phase-halving PLL: circuit diagram 137 C Mixer assembly 141 List of Figures 1.1 Sensitivity of radio telescopes (adapted kom [cl)............ 2 1.2 Large Adaptive Reflector